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This paper proposes an approach for the minimum time swing upof a rotary inverted pendulum. Our rotary inverted pendulum is supported bya pivot arm. The pivot arm rotates in a horizontal plane by means of a servomotor. The opposite end of the arm is instrumented with a joint whose axisis along the radial direction of the motor. A pendulum is suspended at thejoint. The task is to design a controller that swings up the pendulum, keepsit upright and maintains the arm position. In the general intelligent hybridcontroller, a PD controller with a positive feedback is designed for swinging upand a fuzzy balance controller is designed for stabilization. In order to achievethe swing up in a minimal time, a controller named Minimum Time IntelligentHybrid Controller is proposed which is precisely a PD controller together witha pulse step controller for swinging up along with the fuzzy balance controllerfor stabilization. The impulsive control action is tuned by trial and errorto achieve the minimum-time swing-up. An energy based switching controlmethod is proposed to switch over from swing up mode to stabilization mode.Extensive computer simulation results demonstrate that the swing up timeof the proposed minimum-time controller is significantly less than that of theexisting general hybrid nonlinear controller.

We present a new model and a new approach for solving fuzzylinear programming (FLP) problems with various utilities for the satisfactionof the fuzzy constraints. The model, constructed as a multi-objective linearprogramming problem, provides flexibility for the decision maker (DM), andallows for the assignment of distinct weights to the constraints and the objectivefunction. The desired solution is obtained by solving a crisp problemcontrolled by a parameter. We establish the validity of the proposed modeland study the effect of the control parameter on the solution. We also illustratethe efficiency of the model and present three algorithms for solving theFLP problem, the first of which obtains a desired solution by solving a singlecrisp problem. The other two algorithms, interact with the decision maker,and compute a solution which achieves a given satisfaction level. Finally, wepresent an illustrative example showing that the solutions obtained are ofteneven more satisfactory than asked for.

In this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.We also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.

In this paper, we introduce the notions of interval-valued and $(in,ivq)$-interval-valued fuzzy ($p$-,$q$- and $a$-) ideals of BCI algebras and investigate some of their properties. We then derive characterization theorems for these generalized interval-valued fuzzy ideals and discuss their relationship.

We show that the lattice of all ideals of a ring $R$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. For this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (A)$ of a subset $A$ of a ring $R$ forfixed $r , sin [0,1] $ and show that $A$ is an ideal of $R$ if, and only if, its generalizedcharacteristic function $chi _{s}^{r} (A)$ is a fuzzy ideal of $R$. We alsoshow that the set of all generalized characteristic functions $C_{s}^{r}(I(R))$ of the members of $I(R)$ for fixed $r , sin [0,1] $ is acomplete sublattice of the lattice of all fuzzy ideals of $R$ and establishthat this latter lattice is generated by the union of allits complete sublattices $C_{s}^{r} (I(R))$.

In this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. Thena relation between totally fuzzy bounded sets and N-compactness is discussed.Finally, a geometric characterization for fuzzy totally bounded sets in I- topologicalvector spaces is derived.

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